Humanities

... and beyond

Question #f483d

1 Answer

Let us consider that a particle of mass #m# is executing a vertical circular motion,centering the point #O# as shown in figure and having been attached to an in-extensible string of length #R#.

Let #P# represents an arbitrary position of the particle , where the string makes an angle #theta # with the vertical. If #v# be the velocity of the particle at this position then considering forces on the particle we can write

The particle will complete the circle , if the string doesn't slack at the highest point when #theta =180^@# There must be centripetal force to make this happen. The minimum centripetal force required can be had by putting #T_"top"~~0 # in equation [3].

#(m(v_"top"^2)_"min")/R =0+mg#

#=>(v_"top")_min=sqrt(gR).......[5]#

Inserting this value in equation [4] we can get the minimum required velocity of the particle at position #L#